Hi. Now you probably know that if a function f(adsbygoogle = window.adsbygoogle || []).push({}); _{k}(x) converges uniformly to f(x) then we are allowed to certain actions such as

[tex]lim_{n-> \inf}\int f (of k) dx = \int f dx [/tex]

In other words we are allowed to exchange limit and integral. Now say we have any sequnce valued function f_{k}(x) . And we also have

[tex]lim_{n-> \inf}\int f (of k) dx = 0 [/tex]

Does that imply that f_{k}(x) converges uniformly to 0?

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# Inverting Consequences of Uniform Convergence

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